A basic multicarrier transmitter and a corresponding multicarrier receiver as known in the prior art are shown in FIG. 1 of the drawing. Transmitter 10 includes a serial-to-parallel converter 14, a multicarrier modulator 16, and a pretransmit processor 18. Receiver 12 includes a post channel processor 20, a multicarrier demodulator 22, and a parallel-to-serial converter 24. The transmitter and receiver are linked by a digital subscriber line (DSL) or other form of communication channel 26. Serial input data at a rate of b.sub.total /T bits per second are grouped by converter 14 into blocks of b.sub.total bits for each multicarrier symbol, with a symbol period of T. The b.sub.total bits in each multicarrier symbol are modulated in modulator 16 by N separate carriers with b.sub.i bits modulated by the i.sup.-th carrier. The preferred embodiment uses an Inverse Fast Fourier Transform (IFFT) during modulation to generate N.sub.s time-domain samples of a transmit signal for each block of b.sub.total bits, where N.sub.s is preferably equal to 2N. The corresponding multicarrier demodulator performs a Fast Fourier Transform (FFT), where b.sub.i bits are recovered from the i.sup.-th carrier. This particular embodiment of multicarrier modulation is known as the Discrete Multitone (DMT) modulation, and, as depicted in FIG. 2, the carriers in a DMT system are spaced 1/T HZ apart across the lower N/T Hz of the frequency band. More detailed discussion of the principles of multicarrier transmission and reception in general is given by J. A. C. Bingham in "Multicarrier Modulation for Data Transmission: An Idea Whose Time Has Come", IEEE Communications Magazine, Volume 28, Number 5, pp. 5-14, May 1990; and by A. Ruiz et al. in "Discrete Multiple Tone Modulation with Coset Coding for the Spectrally Shaped Channel", IEEE Transactions on Communications, Volume 40, Number 6, pp. 1012-1029, Jun. 1992.
Discrete Multitone Modulation
The general structure of a DMT system is illustrated in FIG. 3, where {X.sub.0,X.sub.1, . . . , X.sub.N-1 } are the original, complex, input data symbols, {x.sub.k } is the modulated data sequence (before cyclic prefix), {h.sub.k } is the discrete-time channel response, {n.sub.k } is the additive noise sequence, {y.sub.k } is the received sequence (after the removal of cyclic prefix), and {x.sub.0, x.sub.1, . . . ,x.sub.N-1 } are the decoded, complex data symbols. The p.sub.i 's and p.sub.i *'s in FIG. 3 are known as the modulating and the demodulating vectors, and preferably they are chosen to be orthonormal. Therefore, for a discrete-time system, the following condition should be satisfied: EQU p.sub.i p*.sub.j *=.delta..sub.ij, (1)
where denotes the dot product of two vectors and the ".delta.-function" is defined as ##EQU1##
For the DMT system, the independent modulating and demodulating vectors in FIG. 3 are the IDFT and the DFT vectors, given by the following pair of relationships: ##EQU2##
A DMT system with N complex subchannels in the frequency domain requires a DFT size of 2N, and the forced conjugate symmetry in the frequency domain will result in the desired real-valued time domain samples. In the preferred embodiment, IDFT and DFT are implemented with the well known IFFT and FFT algorithms. The cyclic prefix is a discrete-time technique (illustrated in FIG. 4) used to eliminate interblock interference (IBI) in the DMT system. More detailed treatments of the cyclic prefix and other finite block length DMT system implementational issues are given by J. S. Chow et al. in "A Discrete Multitone Transceiver System for HDSL Applications", IEEE Journal on Selected Areas in Communications, Volume 9, Number 6, pp. 895-908, Aug. 1991; "Equalizer Training Algorithms for Multicarrier Modulation Systems", 1993 IEEE International Conference on Communications, Geneva, Switzerland, May 1993; and "Method for Equalizing a Multicarrier Signal in a Multicarrier Communication System", U.S. patent application Ser. No. 07/898,104 filed Jun. 1992, issued on Feb. 8, 1994 as U.S. Pat. No. 5,285,474, and assigned to the assignee of the present invention.
FIG. 5a is a block diagram illustrating a communication system including a Central Office Transceiver 27 and a Customer Premises Transceiver linked together by a Duplex Channel 29. Each transceiver includes a transmitter 30 and a receiver 32 that communicates with each other through an operations channel, and each transmitter is linked with a corresponding receiver by a communications channel 34.
FIG. 5b is a more detailed block diagram showing the principal operative components of a basic DMT transmitter 30 and a basic DMT receiver 32 connected through a channel 34. Serial input data are grouped into blocks, converted to a parallel form, and appropriately encoded by an encoder 36. Parallel outputs of the encoder are modulated by an IFFT operation at 38 and converted back to a serial data stream by a converter 40. The digital modulated data stream is cyclically prefixed, converted to analog form by a digital-to-analog converter (DAC) 42, low-pass filtered at 44, and passed through a D.C. isolating transformer 46 during pre-transmit processing to produce an analog transmit signal that is the input to the transmission channel 34.
At the receiver end, the received analog signal is passed through a D.C. isolating transformer and low-pass filter 48, converted to digital form by an analog-to-digital converter (ADC) 50, time domain pre-equalized by a finite impulse response (FIR) filter 52 to limit the effective memory of the channel, and stripped of the cyclic prefix during post-receive processing in converter 54. The resulting digital signals are demodulated by an FFT operation 56 and converted to parallel frequency domain signals. Since the amplitude vs. frequency and the delay vs. frequency responses of the channel are not necessarily constant across the entire used frequency band, the received signal will differ from the transmitted signal, and the parallel inputs to the decoder 58 will differ from those parallel outputs from the encoder 36. A simple form of equalization used to compensate these differences is a frequency domain equalizer (FEQ), which individually adjusts for the attenuation and delay of each of the carriers immediately before the parallel frequency domain signals are passed to the decoder. A one-tap FEQ and decision element is depicted in FIG. 6. Lastly, the frequency domain equalized signals are appropriately decoded and converted back to a serial form by the decoder. Ideally, the detected output serial data from the decoder 58 will be identical to the input serial data to the encoder 36.
Bandwidth Optimization
Due to the dispersive nature of twisted copper pairs, severe channel attenuation as well as intersymbol interference (ISI) are unavoidable in Digital Subscriber Line (DSL) applications. To mitigate the effects of ISI, some sophisticated form of equalization is necessary. Furthermore, the DSL environment consists of a wide variety of loop configurations; as a result, the optimal transmission bandwidth of one particular line may be grossly mismatched to that of another line. To insure best performance, it is then necessary to optimize the transmission bandwidth on a line-by-line basis.
In a conventional single-carrier digital transmission system, such as a Quadrature Amplitude Modulation (QAM) system, implemented with an equalizer or a precoder, the transmission bandwidth is determined by the symbol rate and the carrier frequency of the system. Unfortunately, variable symbol rate, single-carrier systems are still impractical to implement from a complexity standpoint with today's technology, and even if they are implemented, the granularity of possible symbol rates are typically very coarse. This is a direct consequence of the fact that for a fixed data rate, the symbol rate can only change in discrete multiples of b.sub.symbol /(b.sub.symbol .+-.1), where b.sub.symbol is the number of bits transmitted by each data symbol, provided that only signal constellations with integer numbers of bits are used.
Multicarrier modulation, however, offers much more flexibility in terms of granularity because it acts on block symbols that consist of a much larger number of bits per symbol over a large number of carriers. Since different numbers of bits can be transmitted through the different carriers (subchannels), the multicarrier transceiver has complete control of the transmission bandwidth usage. As a result, more data will be transmitted through the better carriers and less data will be transmitted through the worse carriers. (See FIG. 7.) In this manner optimal performance can be achieved, in terms of either maximizing total data throughput for a fixed system performance margin or maximizing overall system performance margin for a fixed target data rate, under a fixed aggregate input power constraint and target bit-error-rate.
The maximum number of bits, b.sub.i, in a 2-dimensional data symbol (see FIG. 8) that can be supported by the i.sup.-th carrier with Signal-to-Noise Ratio (SNR) equal to SNR(i) at a bit-error-rate of P.sub.e, a system performance margin of .gamma..sub.margin, and a total effective coding gain of .gamma..sub.eff is approximately given by the following "gap approximation", which is well known in communication theory (See for example, G. D. Forney, Jr. et al, "Combined Equalization and Coding Using Precoding", IEEE Communications Magazine, Volume 29, Number 12, pp. 25-34, Dec. 1991): ##EQU3## The "SNR gap", .GAMMA., in Equation (5) is defined by: ##EQU4## where the Q-function is defined by: ##EQU5## so Q.sup.-1 (y) is the value of x that satisfies the relationship y=Q(x), and N.sub.e is the number of nearest neighbors in the input signal constellation. For a bit-error-rate of 10.sup.-7 which is common in DSL applications, the "gap approximation" reduces to the following: ##EQU6## Equation (8) will be referred to extensively in the Detailed Description of the Preferred Embodiment of the present application.